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12.94 (1992)

Solved

Let $G$ be a finitely generated pro-$p$-group not involving the wreath product $C_p \wr \mathbb{Z}_p$ as a closed section (where $C_p$ is a cyclic group of order $p$ and $\mathbb{Z}_p$ is the group of $p$-adic integers). Does it follow that $G$ is $p$-adic analytic?

Contributor: A. Shalev

Progress

No, it does not (A. Jaikin-Zapirain, B. Klopsch, J. London Math. Soc. (2), 76, no. 2 (2007), 365–383).

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